Here we will use two example data sets to demonstrate the functions: 1) performing survival analysis using SNP data, and 2) drawing K-M plots using expression-based sample clustering groups. For the first dataset 7 , we will discuss the following dChip analysis steps: SNP data input and normalization, plotting copy number data in the chromosome view, carrying out survival analysis using the log-rank and Cox model, and the permutation function to adjust for multiple testing and assess the genome-wide significance of the survival scores. For the second dataset, we will use a gene expression dataset consisting of 170 uniformly treated patients with multiple myeloma with clinical follow-up of more than five years (Munshi et al., manuscript in preparation). We will first perform unsupervised hierarchical clustering and define gene signatures that classify the samples into sub-groups, and then compare K-M curves by the log-rank test among these sub-groups.

We will use a 192-sample microarray dataset processed on Affymetrix SNP 500 K microarray platform 7 to illustrate the usage of the new analysis and visualization functions. This data set represents 192 uniformly treated patients with multiple myeloma (MM). MM is a common type of hematological cancer and characterized by malignant clonal transformation of plasma cells in bone marrow with excess production of a monoclonal immunoglobulin. Chromosomal aberrations are a hallmark of MM with specific changes (del-13 and t(4;14)) giving poor prognosis and other changes (hyperdiploidy and t(11;14)) conferring better survival 17 .

We use the dChip software to normalize all the arrays of 192 myeloma samples and additional 10 normal blood samples to compute model-based signal values. Normalization and model-based signals are calculated for each of the two sub-arrays and combined. The median genotype call rates are 96.77% and 97.35% respectively for the 250 K Nsp and Sty sub-arrays. A tab-delimited sample information file is prepared with columns specifying survival outcome including survival time and event indicator (0 = alive, 1 = death). Numerical columns are marked in the column header such as "Survival(numeric)", and will be standardized and displayed above the samples in the clustering or chromosome data views. After loading the normalized data into dChip using the menu function "Analysis > Open group", we use the "Tools > Array List File" menu function to create an array list to order samples by the values of a particular sample variable. Array list files are also useful when doing survival analysis on a subset of samples, leaving other samples out of the downstream analysis.

The next step displays the data along chromosomes using the menu function "Analysis > Chromosome" to specify analysis parameters for copy number and LOH analysis (Figure 2). The copy number analysis functions are explained in detail in the dChip manual 14 . When the ploidy of samples are unknown (i.e. tumor samples), we can check the option "Scale copy number mode to 2 copy" to adjust for ploidy effect sample-wise, so that in hyperdiploid samples the chromosomes with normal copy numbers are estimated to have two copies rather than deletion events.

Once the data is displayed by chromosomes, we can toggle between showing individual and all chromosomes using the "Chromosome > Show All" menu. Figure 3 shows the gain and loss of copy numbers in the chromosome view, with SNPs on the rows and samples on the columns. It also uses an array list file to sort all the samples by survival time irrespective of the event indicator. We can browse the genome and quickly observe whether copy gain and loss events are associated with survival. Figure 3 shows that hyperdiploid samples with three copies in chromosome 5 tend to locate on the right side (thus longer survival time) rather than on the left side, suggesting hyperdiploidy is associated with better survival outcome of myeloma patients.

In the first survival analysis function, we use the menu function "Chromosome > Compute Score" to perform genome-wide, single-SNP survival analysis by selecting the "Survival Log-Rank p-value" option under "Scoring method" (Figure 4). It will perform SNP-wise log-rank test for association between copy numbers and survival outcome. The data variables of either event free survival or overall survival can be selected by clicking "Response variable" to open the "Select factors" dialog (Figure 4). For a SNP, all the samples are divided into three groups based on this SNP's inferred copy number: Deletion (≤ 1.5 copy), Gain (≥ 2.5 copy), and "No change" (between 1.5 and 2.5 copy). This copy thresholds are adjustable at the "Options > Score" dialog. The log-rank test is then applied to the three sample groups, testing the null hypothesis that there is no survival difference between the groups.

Across the genome, we compute the log-rank test score for one of every 10 consecutive SNPs to speed up the computation. This is because the inferred copy numbers are correlated for nearby SNPs when computed from 10-SNP local median smoothing, leading to correlated log-rank test scores for nearby SNPs. The window size of 10 is user-adjustable at the dialog option "Tools > Options > Score > Use one of every 10 markers". Once the log-rank test is applied to all the SNPs, dChip will display the survival scores genome-wide (Figure 3). The blue curve on the right displays the negative log10 transformed p-values from the log-rank test, with larger values indicating stronger association between copy numbers and survival outcome. The vertical red line in the gray box indicates the score threshold for the genome-wide significance at the 0.05 level by the MaxT permutation method (see the section below on permutation). One or more regions across the genome could have scores exceeding the threshold. Inspecting the genes within these regions could identify candidate survival-associated genes (Figure 5).

To draw a Kaplan-Meier plot (K-M plot) for an individual SNP, we first click on either a SNP nearby a gene of interest (the menu function "Chromosome > Find Gene" can search for genes) or a SNP from the regions with significant survival scores. Then, we use the "View > K-M plot" function to draw a K-M plot using the copy number data of the SNP to form Deletion, Gain, and "No change" groups as above (Figure 6). The p-value to test the different survival rates between the groups is computed using the log-rank test when there are two or more groups each with 5 or more expected number of events. The SNP (rs16915104) in this K-M plot is within the transcribed region of the PLEKHA5 (PEPP2), an X-linked human homeobox gene at chromosome 12p12.3, which encodes transcription factor with known oncogenic role in cancer and drug resistance via phosphoinositide-mediated signal pathways 18 19 . Using this approach, we can first perform genome-wide screen of SNPs to locate chromosome regions of significant log-rank scores, and then zoom into the peak regions and use K-M plots to check the survival correlation of the SNPs and genes in the region.

The second analysis function performs univariate Cox regression for survival outcome using the inferred copy numbers of SNPs. After calculating and displaying the inferred copy numbers in the chromosome view, we use the menu function "Chromosome > Compute Score" and select the "Survival Cox Regression" option under "Scoring method" to perform univariate Cox regression for individual SNPs across the genome (Figure 4). The computing time will vary depending on the number of samples and SNPs; it takes less than 10 minutes to process the 500 K SNP, 192 sample data on a 2.4 GHz CPU with 3 GB RAM.

This function displays the absolute z-scores computed from the Cox model in the gray box on the right of the copy number view (Figure 3 and 5). Negative z-scores are displayed in blue, indicating less hazard or longer survival as copy number increases: copy number gains are associated with longer survival, or copy number deletions are associated with shorter survival. Positive z-scores are displayed in red, indicating higher hazard or shorter survivals as copy number increases. As before, ordering samples based on survival time visualizes and confirms the association between copy number alteration events and survival variables. Other continuous or binary sample variables can also be selected as "Covariates" to perform multivariate Cox regression to assess the explanatory power of a SNP's copy number to survival in the context of these variables (Figure 4). Permutation can be applied to determine the genome-wide threshold to call chromosome regions significantly associated with survival outcome.

We also extend the existing permutation function in dChip to assess the genome-wide significance of the survival scores derived from the log-rank test or Cox regression. The number of permutation runs is specified at the "Chromosome > Compute Score" dialog (Figure 4). The permutation is computationally intensive but also benefits from computing for only a subset of SNPs across the genome.

The permutation tests the null hypothesis that there is no chromosome region in the cancer genome whose copy number is associated with survival, and therefore any observed association is due to random chance. To simulate data sets under the null hypothesis, we can either permute survival times with censoring indicators across samples or permute chromosome region blocks within every sample. The survival scores from the simulated data sets are then compared to those from the original data set. Specifically for permuting chromosome region blocks, for each sample, whose SNPs are ordered first by chromosomes and then by positions within chromosome, we randomly partition the whole genome into K (≥ 2) blocks, and randomly switch the order of these blocks while preserving the order of SNPs within each block. In this way, the SNPs and their copy numbers in a sample are randomly relocated in blocks to new positions in the genome, while only minimally perturbing the dependence of the copy number data of neighboring SNPs. The same permutation applies to all samples using a different random partition for each sample. The survival score at each SNP locus can then be computed for the permuted data set, and the MaxT method can be applied to assess the significance of the original scores 20 . The maximal survival scores from every permuted data set form the score distribution, whose 95^th largest value is the genome-wide threshold at the 0.05 significance level to determine the chromosome regions significantly associated with survival in the original dataset. Similarly, clinical variables such as survival times and censoring indicators can be permuted together among all the samples and this achieves similar genome-wide significance threshold (Additional file 1: Figure S1 and Additional file 2: Figure S2).

Unsupervised hierarchical clustering is frequently used to discover novel sample sub-groups from microarray data or inspect the expression-based samples clusters in relation to clinical variables. In particular, it is interesting to know whether sample clusters correspond to differential survival outcomes.

We develop a third analysis function in dChip to facilitate drawing K-M plots based on sample clusters. We first use the "Analysis > ANOVA & Correlation" menu to specify the survival variable and event indicator, similar to Figure 4. Next, we use "Analysis > Clustering & Enrichment" menu to cluster samples using a variation-filtered gene list. Interested in whether sample clusters correspond to different survival outcomes, we can click to select a main sample cluster branch (in blue color) and use Control-click to select and color additional sample clusters (Figure 7A). We then use the menu "View/K-M Plot" to display the Kaplan-Meier plot and log-rank p-value based on the specified sample clusters (Figure 7B). The dChip Analysis View will also show the details of log-rank test and the number of samples omitted due to missing survival data.